Go to Settings > Sharing, and drag the Vk.com button to the sharing area.

Enjoy! 🙂

FAQ

Can I use VK’s Like button instead of the Share button?

The Like button requires an app ID and a Vk.com account. To use the Like button you would have to create your own app on Vk.com. I wanted this plugin to be simple to use, so I chose the Share button instead.

Why is this not in Jetpack yet?

If this Jetpack addon becomes popular, I will propose that we add Vk.com in Jetpack’s Sharing module.